Nordic conversions to Christianity occurred over several hundred years, from the 8th to the 11th century. Some conversions were sincere; others were done for economic, political or familial reasons, but often grew into sincere conversions over time. By the 11th century, most Nordic people were baptized Christians. If you read about the lives of the Two Olavs, you will get a good sense of how the Christianization of the Nordic lands came about.
Christianity enhanced the lives of the Nordic peoples. For example, with the introduction of canon law, the status of women improved greatly, as the Church encouraged marriage and fidelity. Unwanted children were no longer placed outside to die, as the Church considered infanticide to be murder. Trading privileges with Christian countries were put in place or improved.